Pinching problem with Solidifier
Quick answer: move your solidify modifier above your subdivision modifier, and give the soldify modifier an edge crease:

Bottom layer: your original.  Selected: my recommendation.  Top: Your object without any modifiers, but with a wireframe.
So the problem here isn't really with your solidify, but with your subdivision, and how it interacts with the shapes you've given it.  It's the subdivision that's pinching, and the solidify is only making that pinch much more apparent.  If you look at the problem area, you're going to see that it's getting screwed up by a quad that is almost degenerate (three verts lie on a line, ie a 180 degree corner), and the only thing making it not degenerate is that it's out of plane with the rest of the quad.  It looks like you're trying to force quad topology onto something without thinking about other characteristics of good topology, and you're paying the price for that.  (This is pretty normal in my experience; the first thing people learn about topology is &quot;Quads!&quot; before they can even say why, and it takes a while to learn anything else.)
What would good topo be for this?  Maybe something like this:

By changing the edge flow, I can maintain quad topology, without any degenerate quads, at the price of a nearly-planar 3-pole.  And we lose that pinch.